Causal Network Discovery from Interventional Count Data with Latent Linear DAGs

TL;DR

This paper introduces a new method for discovering causal networks from interventional count data, accounting for measurement error and latent variables, with proven identifiability and practical validation.

Contribution

It proposes a latent linear Gaussian DAG model with Poisson measurement error and establishes population-level identifiability under intervention, advancing causal discovery methods.

Findings

The model achieves population-level identifiability of the latent causal DAG.

The estimation procedure has theoretical guarantees on error and causal discovery.

Simulations and real data applications demonstrate practical effectiveness.

Abstract

The increasing availability of interventional data offers new opportunities for causal discovery, with gene perturbation studies providing a prominent example. Such data are typically count-valued and subject to substantial measurement error arising from technical variability and latent state heterogeneity. Motivated by these challenges, we study identification and estimation in latent linear structural causal models for interventional count data. We propose a latent linear Gaussian directed acyclic graph (DAG) model with Poisson measurement error that explicitly separates the latent causal structure from the observed counts. Under a mean-shift intervention design, we establish population-level identifiability of the latent causal DAG. Building on these identification results, we develop an estimation procedure based on sparse inverse matrix estimation and provide theoretical guarantees on estimation error and finite-sample causal discovery. Simulation studies and applications to Perturb-seq data demonstrate the practical effectiveness of the proposed method.